多元统计方法在节肢动物群落分析中的应用

近年来有关节肢动物群落的研究报道较多,而传统的、简单的多样性指数分析远远不能满足对高通量群落数据的挖掘。采用多元统计方法可以较好地分析群落数据。其中,在研究某一处理的长期效应时,主响应曲线是一种经典的多元分析方法;而非度量多维尺度分析具有能处理较大量的数据且常能以低维排序图反映结果的优点,是一种具有广泛应用前景的排序技术。本文以Bt棉与非Bt棉不同比例混作棉田的节肢动物群落为例,详尽地介绍了主响应曲线和非度量多维尺度在节肢动物群落分析中的应用。     

Competition and skewness in plantations

Data published recently on the stem diameters in experimental Pinus Radiata plantations, show a skewness which is initially zero, first becomes negative and later reverses direction, becomes positive and increases indefinitely. This and other behaviour are explained using a zone-of-influence model based entirely upon competition between neighbouring trees. Negative skewness can be identified with the early stages of competition when only the largest trees compete. The model also generates bimodal distributions when competition is intense, as observed experimentally in annual plants. Further modes are generated as competition is increased further.     

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log‐normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero‐vectors; (ii) The multivariate zero‐inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero‐truncated/deflated count data and it is difficult to apply to high‐dimensional cases; (iii) The Type I multivariate zero‐adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.     

Measures of precision for dissimilarity‐based multivariate analysis of ecological communities

Ecological studies require key decisions regarding the appropriate size and number of sampling units. No methods currently exist to measure precision for multivariate assemblage data when dissimilarity‐based analyses are intended to follow. Here, we propose a pseudo multivariate dissimilarity‐based standard error (MultSE) as a useful quantity for assessing sample‐size adequacy in studies of ecological communities. Based on sums of squared dissimilarities, MultSE measures variability in the position of the centroid in the space of a chosen dissimilarity measure under repeated sampling for a given sample size. We describe a novel double resampling method to quantify uncertainty in MultSE values with increasing sample size. For more complex designs, values of MultSE can be calculated from the pseudo residual mean square of a permanova model, with the double resampling done within appropriate cells in the design. R code functions for implementing these techniques, along with ecological examples, are provided.     

Negative skewness and negative correlations in spatial competition models

We consider a population of identical biological entities that compete with each other for space and derive, under rather weak assumptions, some statistical properties of the sizes (e.g. biomasses) of the individuals. It is proved, for example, that, during the early stages of competition, their size distribution becomes negatively skewed and the sizes of neighbouring individuals become negatively correlated. The results are proved for a regular periodic array of centres of the individuals where they can be compared with data on plantations.     

The affective impact of financial skewness on neural activity and choice

Few finance theories consider the influence of "skewness" (or large and asymmetric but unlikely outcomes) on financial choice. We investigated the impact of skewed gambles on subjects' neural activity, self-reported affective responses, and subsequent preferences using functional magnetic resonance imaging (FMRI). Neurally, skewed gambles elicited more anterior insula activation than symmetric gambles equated for expected value and variance, and positively skewed gambles also specifically elicited more nucleus accumbens (NAcc) activation than negatively skewed gambles. Affectively, positively skewed gambles elicited more positive arousal and negatively skewed gambles elicited more negative arousal than symmetric gambles equated for expected value and variance. Subjects also preferred positively skewed gambles more, but negatively skewed gambles less than symmetric gambles of equal expected value. Individual differences in both NAcc activity and positive arousal predicted preferences for positively skewed gambles. These findings support an anticipatory affect account in which statistical properties of gambles--including skewness--can influence neural activity, affective responses, and ultimately, choice.     

Joint models for multivariate longitudinal and multivariate survival data

Joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and AIDS clinical trials. We propose a likelihood approach to extend both longitudinal and survival components to be multidimensional. A multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time as well as dependence between different variables. For the survival component of the joint model, we introduce a shared frailty, which is assumed to have a positive stable distribution, to induce correlation between failure times. The proposed marginal univariate survival model, which accommodates both zero and nonzero cure fractions for the time to event, is then applied to each marginal survival function. The proposed multivariate survival model has a proportional hazards structure for the population hazard, conditionally as well as marginally, when the baseline covariates are specified through a specific mechanism. In addition, the model is capable of dealing with survival functions with different cure rate structures. The methodology is specifically applied to the International Breast Cancer Study Group (IBCSG) trial to investigate the relationship between quality of life, disease-free survival, and overall survival.     

Personalized treatment plans with multivariate outcomes

In this work, we propose a novel method for individualized treatment selection when the treatment response is multivariate. Our method covers any number of treatments and it can be applied for a broad set of models. The proposed method uses a Mahalanobis-type distance measure to establish an ordering of treatments based on treatment performance measures. Our investigation in this work deals with means of responses conditional on lower dimensional composite scores based on covariates where these scores are built using single index models to approximate mean responses against patient covariates. Smoothed estimates of such conditional means are combined to construct an estimate of the aforementioned distance measure, which is then used to estimate the optimal treatment. An empirical study demonstrates the performance of the proposed method in finite samples. We also present a data analysis using an HIV clinical trial data to show the applicability of the proposed procedure for real data.